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The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficientmethod for modeling short-pulse laser or relativistic charged particlebeam-plasma interactions. In this algorithm, the plasma response to anon-evolving laser or particle beam is calculated using Maxwell's equationsbased on the quasi-static approximate equations that exclude radiation. Theplasma fields are then used to advance the laser or beam forward using a largetime step. The algorithm is many orders of magnitude faster than a 3D fullyexplicit relativistic electromagnetic PIC algorithm. It has been shown to becapable to accurately model the evolution of lasers and particle beams in avariety of scenarios. At the same time, an algorithm in which the fields,currents and Maxwell equations are decomposed into azimuthal harmonics has beenshown to reduce the complexity of a 3D explicit PIC algorithm to that of a 2Dalgorithm when the expansion is truncated while maintaining accuracy forproblems with near azimuthal symmetry. This hybrid algorithm uses a PICdescription in r-z and a gridless description in $\phi$. We describe a novelmethod that combines the quasi-static and hybrid PIC methods. This algorithmexpands the fields, charge and current density into azimuthal harmonics. A setof the quasi-static field equations are derived for each harmonic. The complexamplitudes of the fields are then solved using the finite difference method.The beam and plasma particles are advanced in Cartesian coordinates using thetotal fields. Details on how this algorithm was implemented using a similarworkflow to an existing quasi-static code, QuickPIC, are presented. The newcode is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks andcomparisons between a fully 3D explicit PIC code, a full 3D quasi-static code,and the new quasi-static PIC code with azimuthal decomposition are alsopresented.

computer physics communications

A quasi-static particle-in-cell algorithm based on an azimuthal Fourier  decomposition for highly efficient simulations of plasma-based acceleration:  QPAD